The force overturning of the iron
2022 Tianfu Cup National Student Mathematical Modeling International Competition
Keywords:
Statics, Dynamics; Conservation of Mechanical Energy; Calculus; Force Analysis; Solid GeometryAbstract
This question is to study the overturning principle of iron. There are two symmetrical iron rings in the diameter direction of an iron pan with uniform mass and density distribution. There are two springs on the iron ring, and there are two iron rings at the other end of the spring. The iron ring is on a smooth bar. On the basis of this model, the overturning principle of iron is studied. From the stem of the first big question, we can see that the characteristics of the first big question are that the spring can only expand but not bend, and the spring is always vertical. According to these characteristics, we solve problem 1 by simple physical analysis; We combine the methods of physical analysis and mathematical calculus to solve problem 2; For problem 3, we use the combination of physical analysis and mathematical calculus to solve it. From the second question, we can see that there are three springs at this time, and we can solve them by physical analysis.
For the first question of question 1, we used the method of college physical mechanics to first establish the static balance model I, and then analyzed the two points with consideration of process quantities, and then established the mechanical balance equation II, which carried out reasonable theoretical proof and derivation of the model. The theoretical proof result is about. Then, with the help of the mathematical algorithm of trigonometric function, we removed the abnormal data, The theoretical results are simulated, and the results show that the theoretical results are consistent with the data simulation results.
For the second question of question 1, we first established the dynamic equation I by using the method of college physical mechanics, then calculated the integral of point B in time considering the amplitude, established the calculus equation II, and carried out reasonable theoretical proof and derivation of the model. The theoretical proof results given are about to sin 0 and sin 0 to , and then removed the abnormal data by using the mathematical algorithm of trigonometric function, The theoretical results are simulated, and the results show that the theoretical results are consistent with the data simulation results.
For the third question of question 1, we first established the dynamic equation I by using the method of college physical mechanics, then calculated the integral of point B in time under the consideration of spring force, established the calculus equation II, conducted reasonable theoretical proof and derivation of the model, and the theoretical proof results given are approximately close to the correct conclusion. Then, with the help of the mathematical algorithm of calculus, we removed the abnormal data, The theoretical results are simulated, and the results show that the theoretical results are consistent with the data simulation results.
For the second question, we first established the mechanical equilibrium stress diagram by using the physical method. On the basis of statics, we first established the model I for equilibrium, and then calculated the integral of the pot in time considering the amplitude, and established the calculus equation II. We conducted reasonable theoretical proof and derivation of the model. The theoretical proof result is about 2357/76. Then, with the help of the mathematical algorithm of calculus, we removed the abnormal data, The theoretical results are simulated, and the results show that the theoretical results are consistent with the data simulation results.
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*******************Cite this Article*******************
APA:
Vochozka, H. (2023). The force overturning of the iron. International Scientific Technical and Economic Research, 1(2), 27–33. http://www.istaer.online/index.php/Home/article/view/No.2308
GB/T 7714-2015:
Vochozka Henning. The force overturning of the iron[J]. International Scientific Technical and Economic Research, 2023, 1(2): 27–33. http://www.istaer.online/index.php/Home/article/view/No.2308
MLA:
Vochozka, Henning. "The force overturning of the iron." International Scientific Technical and Economic Research, 1.2 (2023): 27-33. http://www.istaer.online/index.php/Home/article/view/No.2308
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